{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Neural Network DMD on Slow Manifold\n",
    "\n",
    "Here we will talk about how to use NN-DMD in PyKoopman (`pykoopman.regressor.NNDMD`).\n",
    "In a nutshell, we consider\n",
    "the following model:\n",
    "\n",
    "\\begin{align}\n",
    "z_n &= \\phi(x_n; \\theta_1)\\\\\n",
    "z_{n+1} &= A z_{n}\\\\\n",
    "x_{n+1} &= g(z_{n+1}; \\theta_2)\n",
    "\\end{align}\n",
    "where $\\theta_1, \\theta_2, A$ are trainable parameters.\n",
    "\n",
    "Additionally, we have the following extra control over the model:\n",
    "\n",
    "1. you can choose to change decoder $g$ to be linear.\n",
    "2. $A$ can be further enforced with constraint such that we can guarantee temporal\n",
    "stability\n",
    "3. loss function can include multi-step prediction of the future such that the model\n",
    "can be more accurate\n",
    "4. progressive unrolling can be implemented such that we make the training process\n",
    "more robust"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ways to use NNDMD\n",
    "\n",
    "1. One can certainly use `NNDMD` as a standard \"one-step\" regressor that is feed to\n",
    "the `regressor=` keyword in the koopman model of `pykoopman`. You can think of it as a\n",
    "EDMD but with the nonlinear features tunable to make the lifted system closer to\n",
    "linear system. If you choose this way, we will just use the observables as `Identity()` \n",
    "and we let the NN to do all the nonlinear lifting. You can find examples for the above in `tutorial_koopman_eigenfunction_model_slow_manifold.ipynb`\n",
    "\n",
    "\n",
    "2. Since NNDMD can handle nonlinearity, we could directly use NNDMD (the regressor)\n",
    "alone and skip the `pk.koopman` without the hand-written observables. In this way,\n",
    "you can use `NNDMD.fit` to handle variable length trajectories, which is something I\n",
    "haven't seen in any other packages. \n",
    "\n",
    "In the following, I will demonstrate how to **directly use the regressor NNDMD as a Koopman model**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "outputs": [],
   "source": [
    "import sys\n",
    "sys.path.append('../src')"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pykoopman as pk\n",
    "import numpy as np\n",
    "import numpy.random as rnd\n",
    "np.random.seed(42)  # for reproducibility\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "from pykoopman.common import slow_manifold\n",
    "nonlinear_sys = slow_manifold(mu=-0.1, la=-1.0, dt=0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Collect training data\n",
    "\n",
    "Here I will create a grid between -2 and 2 to sample initial conditions. I sample 51 points along each direction. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_pts = 51\n",
    "xmin = ymin = -2\n",
    "xmax = ymax = +2\n",
    "xx, yy = np.meshgrid(np.linspace(xmin, xmax, n_pts), np.linspace(ymin, ymax, n_pts))\n",
    "Xdat = np.vstack((xx.flatten(), yy.flatten()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, I will generate many sequence with different length"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "max_n_int = 51\n",
    "\n",
    "traj_list = []\n",
    "for i in range(Xdat.shape[1]):\n",
    "    X, Y = nonlinear_sys.collect_data_discrete(Xdat[:,[i]], np.random.randint(1, max_n_int))\n",
    "    tmp = np.hstack([X, Y[:,-1:]]).T\n",
    "    traj_list.append(tmp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "Text(0.5, 1.0, 'we can handle trajectory data with varying-length sequence!')"
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 1200x400 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,4))\n",
    "plt.bar(np.arange(len(traj_list)), [len(x) for x in traj_list])\n",
    "plt.xlabel('index of trajectory')\n",
    "plt.ylabel('number of points in each sequence')\n",
    "plt.title('we can handle trajectory data with varying-length sequence!')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we call NNDMD as our model\n",
    "\n",
    "1. Note that we call `look_forward=50`, which means our model can **at most** handle data sequence with 51 points.\n",
    "2. If the data sequence contain more than 51 points, if can still set `look_forward=50`, or even smaller number. \n",
    "3. But you cannot set `look_forward` to be larger than the `length_of_longest_sequence`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "look_forward = 50\n",
    "dlk_regressor = pk.regression.NNDMD(dt=nonlinear_sys.dt, look_forward=look_forward,\n",
    "                                    config_encoder=dict(input_size=2,\n",
    "                                                        hidden_sizes=[32] * 3,\n",
    "                                                        output_size=3,\n",
    "                                                        activations=\"swish\"),\n",
    "                                    config_decoder=dict(input_size=3, hidden_sizes=[],\n",
    "                                                        output_size=2, activations=\"linear\"),\n",
    "                                    batch_size=512, lbfgs=True,\n",
    "                                    normalize=True, normalize_mode='equal',\n",
    "                                    normalize_std_factor=1.0,\n",
    "                                    trainer_kwargs=dict(max_epochs=3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just like before, use `.fit`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO: GPU available: True (cuda), used: True\n",
      "[rank_zero.py:64 -                _info() ] GPU available: True (cuda), used: True\n",
      "INFO: TPU available: False, using: 0 TPU cores\n",
      "[rank_zero.py:64 -                _info() ] TPU available: False, using: 0 TPU cores\n",
      "INFO: IPU available: False, using: 0 IPUs\n",
      "[rank_zero.py:64 -                _info() ] IPU available: False, using: 0 IPUs\n",
      "INFO: HPU available: False, using: 0 HPUs\n",
      "[rank_zero.py:64 -                _info() ] HPU available: False, using: 0 HPUs\n",
      "INFO: You are using a CUDA device ('NVIDIA GeForce RTX 3080 Ti Laptop GPU') that has Tensor Cores. To properly utilize them, you should set `torch.set_float32_matmul_precision('medium' | 'high')` which will trade-off precision for performance. For more details, read https://pytorch.org/docs/stable/generated/torch.set_float32_matmul_precision.html#torch.set_float32_matmul_precision\n",
      "[rank_zero.py:64 -                _info() ] You are using a CUDA device ('NVIDIA GeForce RTX 3080 Ti Laptop GPU') that has Tensor Cores. To properly utilize them, you should set `torch.set_float32_matmul_precision('medium' | 'high')` which will trade-off precision for performance. For more details, read https://pytorch.org/docs/stable/generated/torch.set_float32_matmul_precision.html#torch.set_float32_matmul_precision\n",
      "INFO: LOCAL_RANK: 0 - CUDA_VISIBLE_DEVICES: [0]\n",
      "[cuda.py:58 -     set_nvidia_flags() ] LOCAL_RANK: 0 - CUDA_VISIBLE_DEVICES: [0]\n",
      "INFO: \n",
      "  | Name                | Type                    | Params\n",
      "----------------------------------------------------------------\n",
      "0 | _encoder            | FFNN                    | 2.3 K \n",
      "1 | _decoder            | FFNN                    | 6     \n",
      "2 | _koopman_propagator | StandardKoopmanOperator | 9     \n",
      "3 | masked_loss_metric  | MaskedMSELoss           | 0     \n",
      "----------------------------------------------------------------\n",
      "2.3 K     Trainable params\n",
      "0         Non-trainable params\n",
      "2.3 K     Total params\n",
      "0.009     Total estimated model params size (MB)\n",
      "[model_summary.py:83 -            summarize() ] \n",
      "  | Name                | Type                    | Params\n",
      "----------------------------------------------------------------\n",
      "0 | _encoder            | FFNN                    | 2.3 K \n",
      "1 | _decoder            | FFNN                    | 6     \n",
      "2 | _koopman_propagator | StandardKoopmanOperator | 9     \n",
      "3 | masked_loss_metric  | MaskedMSELoss           | 0     \n",
      "----------------------------------------------------------------\n",
      "2.3 K     Trainable params\n",
      "0         Non-trainable params\n",
      "2.3 K     Total params\n",
      "0.009     Total estimated model params size (MB)\n"
     ]
    },
    {
     "data": {
      "text/plain": "Training: 0it [00:00, ?it/s]",
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "002739e671674cc1970b241d6feac6bb"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO: `Trainer.fit` stopped: `max_epochs=3` reached.\n",
      "[rank_zero.py:64 -                _info() ] `Trainer.fit` stopped: `max_epochs=3` reached.\n"
     ]
    }
   ],
   "source": [
    "dlk_regressor.fit(traj_list)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, with recurrent loss minimized, eigenvalues matches perfectly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.998477   -0.20009601 -0.0999843 ]\n"
     ]
    }
   ],
   "source": [
    "eigv = np.log(dlk_regressor.eigenvalues_)/nonlinear_sys.dt\n",
    "print(eigv)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Testing on unseen trajectory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "x0 = np.array([2, -4])  #np.array([2, -4])\n",
    "T = 20\n",
    "t = np.arange(0, T, nonlinear_sys.dt)\n",
    "Xtest = nonlinear_sys.simulate(x0[:, np.newaxis], len(t)-1).T\n",
    "Xtest = np.vstack([x0[np.newaxis, :], Xtest])\n",
    "\n",
    "Xkoop_nn = dlk_regressor.simulate(x0[np.newaxis, :], n_steps=len(t)-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "<matplotlib.legend.Legend at 0x19edbe8f910>"
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 400x400 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(4,4))\n",
    "for i in range(len(traj_list)):\n",
    "    plt.plot(traj_list[i][:,0],traj_list[i][:,1],'-k',alpha=0.05)\n",
    "plt.plot(Xtest[:,0],Xtest[:,1],'-r',lw=3,label='test')\n",
    "plt.plot(Xkoop_nn[:,0],Xkoop_nn[:,1],'--b',lw=2.5,label='nndmd')\n",
    "\n",
    "plt.xlabel(r\"$x_1$\",size=20)\n",
    "plt.ylabel(r\"$x_2$\",size=20)\n",
    "plt.title(f\"number of training trajectories = {len(traj_list)}\",size=15)\n",
    "plt.legend(loc='best',fontsize=15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can check out the transformation $\\phi_i(x)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create some grid\n",
    "n_pts = 501\n",
    "xmin = ymin = -2\n",
    "xmax = ymax = +2\n",
    "xx, yy = np.meshgrid(np.linspace(xmin, xmax, n_pts), np.linspace(ymin, ymax, n_pts))\n",
    "Xdat = np.vstack((xx.flatten(), yy.flatten()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# compute the transformation (real numbers)\n",
    "transf = dlk_regressor._compute_phi(Xdat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 1100x300 with 6 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,axs=plt.subplots(1,3,figsize=(11,3))\n",
    "for i in range(3):\n",
    "    im = axs[i].contourf(xx,yy,transf[i].reshape(n_pts, n_pts),cmap='RdBu',levels=50)\n",
    "    axs[i].set_title(f\"$\\phi_{i}$\")\n",
    "    axs[i].set_xlabel(r\"$x_1$\")\n",
    "    axs[i].set_ylabel(r\"$x_2$\")\n",
    "    fig.colorbar(im,ax=axs[i])\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "More interestingly, we can also check out the eigenfunctions $\\psi_i(x)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create some grid\n",
    "n_pts = 501\n",
    "xmin = ymin = -2\n",
    "xmax = ymax = +2\n",
    "xx, yy = np.meshgrid(np.linspace(xmin,xmax, n_pts), np.linspace(ymin, ymax, n_pts))\n",
    "Xdat = np.vstack((xx.flatten(), yy.flatten()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# compute the eigenfunction\n",
    "eigf = dlk_regressor._compute_psi(Xdat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 1100x300 with 6 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,axs=plt.subplots(1,3,figsize=(11,3))\n",
    "for i in range(3):\n",
    "    axs[i].contourf(xx,yy,eigf[i].reshape(n_pts, n_pts),cmap='RdBu',levels=50)\n",
    "    axs[i].set_title(f\"$\\psi_{i}$ with $\\lambda_{i}$ = {eigv[i]:.4f}\")\n",
    "    axs[i].set_xlabel(r\"$x_1$\")\n",
    "    axs[i].set_ylabel(r\"$x_2$\")\n",
    "    fig.colorbar(im,ax=axs[i])\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also get the mapping that maps $\\phi(x)$ back to $x$, so let's verify $x=C\\phi(x)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# just consider random state x, let's verify we can get x back\n",
    "x = np.random.rand(100,2)*2-1\n",
    "phi = dlk_regressor.phi(x_col=x.T)\n",
    "x_rec = dlk_regressor.C @ phi\n",
    "\n",
    "# verification using 0.1% deviation error as criterion\n",
    "assert np.linalg.norm(x_rec-x.T)/np.linalg.norm(x) < 1e-2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, let's verify $x = V \\psi(x)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.random.rand(100,2)*2-1\n",
    "psi = dlk_regressor.psi(x_col=x.T)\n",
    "x_rec = dlk_regressor.W  @ psi\n",
    "\n",
    "# verification using 0.1% deviation error as criterion\n",
    "assert np.linalg.norm(x_rec-x.T)/np.linalg.norm(x) < 1e-2"
   ]
  }
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